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A Generalization of SAT and #SAT for Robust Policy Evaluation (CMU-CS-13-107)

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journal contribution
posted on 01.01.2001, 00:00 by Erik Zawadski, Andre Platzer, Geoffrey J. Gordon

Both SAT and #SAT can represent difficult problems in seemingly dissimilar areas such as planning, verification, and probabilistic inference. Here, we examine an expressive new language, #∃SAT, that generalizes both of these languages. #∃SAT problems require counting the number of satisfiable formulas in a concisely-describable set of existentially quantified, propositional formulas. We characterize the expressiveness and worst-case difficulty of #∃SAT by proving it is complete for the complexity class #P NP[1], and relating this class to more familiar complexity classes. We also experiment with three new general-purpose #∃SAT solvers on a battery of problem distributions including a simple logistics domain. Our experiments show that, despite the formidable worst-case complexity of #P NP[1], many of the instances can be solved efficiently by noticing and exploiting a particular type of frequent structure.